When solving the equation 12x^2 - 7x = 6-2(x^2 - 1). Evan wrote 12x^2 - 7x = 6 - 2x^2 + 2 as his first step. Which property
justifies this step?

a. subtraction property of equality
b. multiplication property of equality
c. associative property of multiplication
d. distributive property of multiplication over subtraction​

Answer:

12.5

Step-by-step explanation:

7:56*100 =

(7*100):56 =

700:56 = 12.5

ANSWER

[tex](b + 3)(1 - c)[/tex]

EXPLANATION

The given expression is:

[tex](b + 3) - c(b + 3)[/tex]

We can rewrite this to reveal the invisible 1 multiplying the first term.

[tex]1(b + 3) - c(b + 3)[/tex]

There is a common factor of (b+3).

We factor to get;

[tex](b + 3)(1 - c)[/tex]

Therefore the completely factored form of the given expression is

[tex](b + 3)(1 - c)[/tex]

Answer:

g(4) = 11

Step-by-step explanation:

x = 4

4(2) + 3 = 11

Answer:

19

Step-by-step explanation:

Replace the x with four

Arranging it in ascending order:

1, 2, 2, 3, 3, 4, 7, 7, 7, 9

Mode is most frquently occuring observation..

i.e. Here ,7 Occurs the most(thrice)

So mode= ,7

Hello There!

Mode: The number that occurs most often in a set of numbers.

Although it's optional, I like to put the numbers from least to greatest because it can be easier to see what number occurs the most.

-Least To Greatest-

1 - 2 - 2 - 3 - 3 - 4 - 7 - 7 - 7 - 9

When we look at our set of data, we can notice that the number 7 appears the most so the mode for out set of data is 7.

Mode =  7

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

An exponential function is one in which a term has been raised to a particular power as we can see in the options given.

The fastest rate for larger values of x will be observed in the function  f(x)=5^x + 2.

Learn more about exponential function:https://brainly.com/question/11487261

#SPJ2

To calculate the cost per cup of bleach, first convert the quantity from gallons to cups. A 3-gallon bottle equals 48 cups. Divide the total cost ($13.92) by the total number of cups (48) to determine the cost per cup, which is $0.29.

This problem involves finding out the unit cost or, in this case, the cost per cup of bleach. One gallon is equivalent to 16 cups, hence a 3-gallon bottle is equivalent to 48 cups.

So, if $13.92 buys you 48 cups, you can calculate the cost per cup by dividing the total cost by the number of cups.

Proceed with the following calculation: $13.92 costs /48 cups = $0.29 per cup of bleach costs.

In conclusion, each cup of bleach from this 3-gallon bottle would cost you $0.29.

https://brainly.com/question/31310172

#SPJ2

To find the price per cup of bleach from a 3-gallon bottle costing $13.92, we multiply 3 gallons by 16 cups per gallon to get 48 cups, and then divide $13.92 by 48 to find the cost per cup, which is approximately $0.29.

To calculate the price per cup of bleach when given the price per gallon, we need to know how many cups are in a gallon and then divide the total cost by the total number of cups.

First, we establish that there are 16 cups in a gallon. Since we are dealing with a 3-gallon bottle, the total number of cups will be 3 gallons times 16 cups per gallon, which equals 48 cups.

Next, we take the total cost of the 3-gallon bottle, which is $13.92, and divide it by the total number of cups, 48. Performing this division gives us the cost per cup. So, $13.92 divided by 48 cups equals approximately $0.29 per cup.

This method demonstrates how to break down bulk costs into more manageable unit prices and can be applied across various products and measurements.

Answer:

AC=16.2 units

Step-by-step explanation:

we know that

The triangle ABC is an isosceles triangle

so

AX=XC

because triangles ABX and CBX are congruents

AC=2*AX

see the attached figure to better understand the problem

therefore

AC=2*8.1=16.2 units

Final answer:

To find the length of AC, we add the lengths of segments AX and BC, giving us AC = 8.1 + 18.5, which equals 26.6 units.

Explanation:

If we are given that AB = 18.5 units, AX = 8.1 units, and BC = 18.5 units, then to find the length of AC, we simply need to add the lengths of segments AX and BC together, since AX and BC are adjacent segments on line AC. The formula to calculate AC in this situation is:

AC = AX + BC

Substituting the given values into this formula gives us:

AC = 8.1 units + 18.5 units = 26.6 units

Therefore, the length of segment AC is 26.6 units.

Answer:

8

Step-by-step explanation:

The number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1 are:

                               36

We are asked to find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

We know that a number is even if the last digit of the number is divisible by 2 i.e. even.

Hence, the only digits among the given digits which is even is: 8

Now, at the first place any of the 6 digits could come up.

( Since, the digits could be repeated)

Also, at the second palace any of the 6 digits could come up.

Hence, the total number of such numbers possible are:

                 6×6×1=36

Answer:

You got it right.

Step-by-step explanation:

Answer:

The discriminant is -23 and the equation has no real roots.

Step-by-step explanation:

Since, the discriminant of the quadratic equation [tex]ax^2+bx+c=0[/tex]

is,

[tex]D=b^2-4ac[/tex]

If D > 0, then the equation has two distinct real roots,

if D = 0, then the equation has two equal real roots,

if D < 0 then the equation has no real roots,

Here, the quadratic equation is,

[tex]x^2+3x+8=0[/tex]

Discriminant,

[tex]D=3^2-4\times 1\times 8=9-32 = -23 < 0[/tex]

Therefore, the discriminant is -23 and the equation has no real roots.

Answer:

50.265

Step-by-step explanation:

Answer:

B. 25

Step-by-step explanation:

We can use the altitude theorem, to quickly find the value of x.

According to this theorem; the altitude  of the triangle is equal to the geometric mean of the product of the two segments created by the leg of the altitude on the hypotenuse.

We apply this theorem to obtain:

[tex]10=\sqrt{4x}[/tex]

This implies that:

[tex]10^2=4x[/tex]

[tex]100=4x[/tex]

Divide both sides by 4 to obtain:

[tex]\frac{100}{4}=x[/tex]

[tex]x=25[/tex]

Answer:

reflect across the y-axis; rotate 180° counterclockwise about the origin - first choice

Answer:

Option A.

Step-by-step explanation:

The graph below shows the transformation from triangle 1 to triangle 2 as below.

1). To understand the transformation we will take a point A. Present coordinates of point A are (1, -1).

When point A is reflected across y - axis, coordinates of A' become (1, 1).

2). Now we see that triangle 2 is in 3rd quadrant having coordinates A"(-1, -1)

which reveals that A'(1, 1) has been rotated by 180° counterclockwise.

Therefore, option A. is the correct choice.

Answer:  B) 160

Step-by-step explanation:

Since the Standard deviation of 21 bins is 3 bins, then the first 7 bins falls in the first 2.5% edge of the bell curve.

2.5% of 21 times 1000 = (0.025)(21)(1000) = 160

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=40ft,\ leg=30ft,\ hypotenuse=x[/tex]

Substitute:

[tex]40^2+30^2=x^2\\\\1600+900=x^2\\\\2500=x^2\to x=\sqrt{2500}\\\\x=50\ ft[/tex]

You can see that you have a right triangle in the figure is a right triangle, which means that you can find the hypotenuse using the Pythagorean theorem:

[tex]d = \sqrt{30^2+40^2}=\sqrt{900+1600}=\sqrt{2500} = 50[/tex]

Answer:

Angles in a triangles add up to 180°

Respectively 1 : 2 : 3 is going to be 1 x , 2 x and 3 x so,

1 x + 2 x + 3 x = 180°

⇒ Simplify

6 x = 180°

⇒ Divide by 6 on both sides to isolate x

x = 30°

Since the ratio was 1 x : 2 x : 3 x and x is 30°,

30 : 60 : 90

And since there is a 90° angle, it is a right - angled triangle

ANSWER

[tex]\sqrt{5} [/tex]

EXPLANATION

The given radical expression is

[tex]5 \div \sqrt{5} [/tex]

This can be rewritten as

[tex] \frac{5}{ \sqrt{5} } [/tex]

We rationalize the denominator to get:

[tex]\frac{5}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } [/tex]

Recall that

[tex] \sqrt{x} \times \sqrt{x} = x[/tex]

This implies that,

[tex] \frac{5 \sqrt{5} }{5} [/tex]

Cancel out the common factors to get,

[tex] \sqrt{5} [/tex]

Jared is correct because if you substitute a random number in for x 2 for example

2+10=12

2-10 doesn’t =12

Answer:

Both Jared and Nicole are correct. You can solve for either variable and use the equivalent expression to create a one-variable equation. Then you can solve. Jared would have created a one-variable equation that can be used to solve for x, whereas Nicole would have created a one-variable equation that can be used to solve for y.

Step-by-step explanation:

Answer:

A. A tennis tournament in which after each round, half the players are eliminated.

Step-by-step explanation:

Answer:

1/2x-5=13

Step-by-step explanation:

Let x= Frankie’s mother’s age

Half his mother’s age= 1/2x

5 less than that=1/2x-5

We know that Frankie is 13 so that equation is equal to Frankie’s age, which is 13.

Hope this helps.

To determine Franky's mother's age, we can create an equation using the given information. By solving the equation, we find that Franky's mother is 36 years old.

To determine Franky's mother's age, we can create an equation based on the given information. Let's assume Franky's mother's age is M. According to the information given, Franky's age is 5 years less than half of his mother's age. So, Franky's age can be represented as (1/2)M - 5.

We are also given that Franky is 13 years old. So we can set up the equation:

(1/2)M - 5 = 13

To solve for M, we can simplify the equation:

(1/2)M = 13 + 5

(1/2)M = 18

M = 18 * (2/1)

M = 36

Therefore, Franky's mother's age is 36 years old.

Answer:

[tex]y(t) = 750 -50t[/tex]

Step-by-step explanation:

We want to model the position of the submarine as a function of time.

Notice that we have a constant amount. The initial depth: 750 meters

 Then we have a factor that varies over time. Every hour the submarine ascends 50 meters. therefore as t increases the depth y(t) of the submarine decreases. Then the factor is:

-50t.

Where t represents the time in hours.

Then the equation that represents the new position of the submarine in relation to the level of the sea:

[tex]y(t) = 750 -50t[/tex]

Answer:

im pretty sure it's -750 + 4 x 50

Step-by-step explanation:

This is the only answer that really makes sense to me

Answer:

$50

Step-by-step explanation:

So that means 40 percent is equal to $20 do

40:20

Divided by 2

20:10

Times 5

100:50

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

Answer:

You have to scale the bigger triangle to a small one with ratio of 1.1 to 4.4,  [tex]\frac{1.1}{4.4\\}[/tex]

the ratio is 1/4

the scale factor is 0.25 , so the statement is true

Answer:40.85

Step-by-step explanation:

43x5/100=2.15

43-2.15= 40.85

Answer:

The sale-price of this dress is $40.85

Step-by-step explanation:

Multiply 95 by 43 (since the dress is 5% off, it 95% of it's normal sales price). Divide that number by 100:

(95 × 43) ÷ 100

let's bear in mind that 1 Cup = 8 fl oz.

a) is absolutely correct, 18oz and thus they can fit fine in the 24oz container.

b) is correct, 24 - 18 = 6, we can fit in 6 more oz, which is 3/4 of a cup.

c) is correct as well

d)

we just need to convert c) units to fluid ounces

[tex]\bf 2\frac{1}{4}\implies \cfrac{9}{4}\cdot 8\implies \boxed{18}~\hfill 3\cdot 8\implies \boxed{24} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{juice}}{18}+\stackrel{\textit{water}}{12}+\stackrel{\textit{ice cream}}{24}\implies 54~\textit{fluid ounces}[/tex]

Answer:

C, and D are both roots of this equation

Answer:

The two values of x that are roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

Step-by-step explanation:

A cuadratic function has the form [tex]ax^{2} + bx +c = 0[/tex]

To calculate the roots of the cuadratic equation [tex]x^{2} + 3x -3 = 0[/tex] you have to solve the formula:

[tex]x = \frac{-b}{2a}[/tex] ±[tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case, a =1, b=3 and c= -3

Replacing the values of a,b and c in the formula:

[tex]x = \frac{-3}{(2)(1)}[/tex] ± [tex]\frac{\sqrt{(3)^{2} - (4)(1)(-3) } }{(2)(1)}[/tex]

Solving the mathematic operations:

x = [tex]\frac{-3}{2}[/tex] ± [tex]\frac{\sqrt{9 + 12 } }{2}[/tex]

The two roots are:

[tex]x_{1} = \frac{-3 + \sqrt{21} }{2}[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{21} }{2}[/tex]

Answer:

Assuming that you're calculating surface area it would be:

16+10+10+10+10 or B

Step-by-step explanation:

The answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

To find the required function f(3), we need to use the given function f(x) and evaluate "x" equal to 3 (input).

We are given the function:

[tex]f(x)=(\frac{1}{6})^{x}[/tex]

Then, evaluating "x" equal to 3, we have:

[tex]f(3)=(\frac{1}{6})^{3}[/tex]

[tex]f(3)=(\frac{1}{6})^{3}=(\frac{1}{6})*(\frac{1}{6})*(\frac{1}{6})=(\frac{1}{6*6*6})[/tex]

[tex]f(3)=(\frac{1}{6*6*6})=(\frac{1}{216})[/tex]

Hence, we have that the answer is:

[tex]f(3)=(\frac{1}{216})[/tex]

Have a nice day!

Answer: 432ft. shadow

Step-by-step explanation:

Because Nora is 5’3”, you need to convert every numerical value into inches by multiplying them by 12 (12in = 1 ft.)

5’ x 12 = 60” + 3” = 63”

9’ x 12 = 108”

252’ x 12 = 3,024”

Then create equivalent fractions.

63/108 = 3,024/x

108 x 3024 = 326,592/63 = 5,184in.

Then convert it back into feet.

5,184/12 = 432ft.

Final answer:

Using the proportion of similar triangles, we find that if Nora, who is 63 inches tall, casts a 108-inch shadow, then the 3024-inch tall monument will cast a shadow that is 5184 inches long, or 432 feet.

Explanation:

To find the length of the shadow casted by the monument, we can use the concept of similar triangles. The proportion between the heights and shadows of Nora and the monument will be the same because the angle of the sunlight is the same for both. Nora is 5'3" tall, which is 63 inches, and she casts a 9-foot shadow, which is 108 inches. The monument is 252 feet tall, which is 3024 inches. Setting up the proportion, we have:

Nora's height : Nora's shadow = Monument's height : Monument's shadow

63 inches : 108 inches = 3024 inches : x inches

To solve for x (the length of the monument's shadow in inches), we cross-multiply and divide:

63 * x = 3024 * 108

x = (3024 * 108) / 63

x = 5184 inches

To convert this back to feet, we divide by 12 inches per foot:

x = 5184 inches / 12 inches/foot

x = 432 feet

Therefore, the length of the shadow cast by the monument is 432 feet.

Answer:

3x+2y=5

2y=5-3x

y=5/2-3/2x

Or you can write as:

y=2.5-1.5x

Answer: y=3/5x+5/2

Step-by-step explanation:

Answer:

$0.036

Step-by-step explanation:

I will be solving this questions in a rational, proportional way.

This question given is directly proportional. There are two types of proportion.

Direct - Let's say there are two values, x and y. In direct proportion, while x   increases, y increases with it.  

Inverse- Taking x and y, in inverse proportion, while x increases, y decreases or while y increases, x decreases.

In the given example, there are two values, number of plates and cost of plates. While the number of plates increases, the cost would surely increase. Therefore, giving us that it is a direct proportion.

500 plates : $18.00 :: 1 : $x

500 plates is to 18 dollars, then, 1 plate is to how many dollars?

In direct proportion, the product of extremes is equal to the product of means.

500(x) = 18(1)

500x = 18

x = 18 / 500

x = 0.036

Hence, one plate costs $0.036 or 3.6 cents

Answer:

each plate cost:  .036 each

18.00 divided by 500

Step-by-step explanation: